EP3833515A1

EP3833515A1 - Method for estimating a wrench

Info

Publication number: EP3833515A1
Application number: EP18755427.4A
Authority: EP
Inventors: Debora CLEVER; Fan Dai; Hao Ding; Tomas Groth; Dr. Björn MATTHIAS; Arne WAHRBURG
Original assignee: ABB Schweiz AG
Current assignee: ABB Schweiz AG
Priority date: 2018-08-09
Filing date: 2018-08-09
Publication date: 2021-06-16
Also published as: US20210162596A1; WO2020030272A1; US11279027B2; CN112533738A

Abstract

The invention is about a method for estimating a wrench acting on a reference point of a robot, comprising the steps of a) measuring at least one, but not all components of the wrench, and b) estimating non-measured components of the wrench based on a dynamical model of the robot while taking the measured components into account

Description

ABB Schweiz AG

Method for estimating a wrench

The present invention relates to a method for esti mating a wrench acting on a reference point of a robot, such as its tool center point, TCP.

In robotics, a wrench is a six-dimensional vector, of which three components describe a force acting on the reference point, and three more component define a torque which is applied to said same point.

If industrial robots are to operate in a force- controlled manner, they are typically equipped with a 6 degrees of freedom (DOF) force/torque (F/T) sensor that measures both contact forces in three translational directions and contact torques about all three axes. Based on this information, the con tact forces and torques can actively be controlled in one or several directions, e.g. for assembly, grinding, or polishing. While 6 DOF F/T measurement provides high quality F/T information, the sensors that are required for the purpose are expensive.

As an alternative to measuring, contact forces and torques can also be estimated based on a dynamic model of the robot. Such estimation of forces and torques requires no force and torque sensors; the only input that is required are data that define angles of the various joints of the robot, and data on motor current or any other data from which motor torque can be calculated. Since these data are needed for controlling any movement of the robot, force-controlled or not, devices that provide them are generally present in a robot system and can be used for providing input to the dynamic model at no further cost.

The quality of the estimated forces and torques de- pends heavily on the precision with which the dy namic model of the robot allows to predict friction in the joints of the robot. This prediction can be difficult, since there are many parameters of the robot which have an influence on friction but which may not all be known, or which cannot be measured or predicted with the desired precision.

The object of the present invention is to provide a method for estimating a wrench which can achieve a high precision at low cost.

This object is achieved by a method comprising the steps of

a) measuring at least one, but not all components of the wrench, typically using a built-in sensor of the robot , and

b) estimating non-measured components of the wrench based on a dynamical model of the robot while taking the measured components into account.

The cost of implementing the method can be kept low not only because the overall number of sensors can be reduced in comparison with the 6 DOF F/T meas urement approach, but also because the component (s) of the wrench that are chosen to be measured can be the one(s) which offer the best ratio of cost to efficiency. For example, measuring a force may be preferable over measuring a torque since a precise torque measurement may require a certain distance between a force-sensitive element and an axis relative to which the torque is measured, while a force meas- urement does not, so that a force sensor can fit into a smaller space.

From the viewpoint of cost and efficiency, no addi tional sensor can improve the precision of the wrench estimation more than the first sensor does. Therefore, in a preferred embodiment, the number of measured components is 1.

Further, it is preferred that the measured compo- nent is parallel to a surface normal of a surface of the robot which extends through the reference point. In that way, a contact force between the ro bot and an outside object touching the surface can be measured precisely, and there is no risk of the measurement being distorted by the object slipping along the surface. Alternatively, it can be paral lel to a direction in which the reference point ad vances when processing a workpiece, so that during processing, pressure exercised on the workpiece can be measured precisely.

There are various approaches by which the measured component (s) can be taken account of. One of these is to estimate the non-measured compo nents by a maximum- likelihood estimation, i.e. by finding those values of the non-measured components for which the likelihood of measuring the values of the measured components that actually were measured is highest.

Another is based on the principle of the Kalman filter. A Kalman filter can be set up having the coordinates and speeds of the robot in the various degrees of freedom as its state. The at least one measured component is input as a state measurement into said Kalman filter, so that it will be taken into account when a future state is predicted based on the measured state of the Kalman filter.

Still another approach comprises, as substeps of step b) , steps of calculating a first estimate of the wrench based on the dynamical model alone, and of refining the first estimate using a maximum-a- posteriori estimation.

Further features and advantages of the invention will become apparent from the following description of embodiments thereof, referring to the appended drawing .

Fig. 1 is a schematic view of a robot system to which the invention is applicable.

The robot system of Fig. 1 comprises a robot arm 1 and an associated controller 2. The robot arm 1 comprises a base 3, an end effector 4, an arbitrary number of links 5i, i=l, 2, ... and joints 6j , j=l, 2, ... which connect the links 5i to each other, to the base 3 or to the end effector 4. For the sake of simplicity it will be assumed here that each joint has one degree of rotational freedom, i.e. is rotatable around a single axis 7. A given link 5i can be rotatable with respect to a neighbouring link 5(i+l) or 5(i-l) about two different axes; in that case -although the connection might in prac tice be formed by a single ball joint - it will be assumed here that the links are connected by two joints, each having one degree of rotational free dom.

Each such joint 6j comprises a motor to drive its rotation and a rotational encoder for feeding back the rotation angle of the joint 6j to controller 2.

The end effector 4 is a tool of any desired type, such as a gripper, a welding or soldering tool, a machining tool, a grinding tool etc, or, in the ex ample of Fig. 1, a drill. The drill comprises a drilling head 8 and a socket 9 in which the drill ing head 8 is removably mounted and is rotatably driven around an axis 7 and advances along axis 7 during drilling. The socket 9 accomodates a force sensor 10 which is designed to detect a force com ponent along axis 7.

As is well known, external forces and torques at a tool center point (TCP) 11 such as the tip of drilling head 8 induce joint load torques according to

where is the manipulator TCP Jacobian with respect to the base frame. We partition the wrench /e K⁶ into / =f_{m +}f_nm , where f_m contains the compo nents that can directly be measured by available low-dimensional sensors of the robot, i.e. by sen sor 10 in the case of Fig. 1, and f_nm contains com ponents which cannot be measured because the robot arm 1 lacks appropriate sensors . Assuming that the direction of axis 7 is the z direction, f and f can be written

Replacing f by f_{m +}f_nm in eq. (1) , we can write define

f_nm (3)

Since f_nm has at least one component which is zero (corresponding to the measured component of f_{m )} , eq. (3) can be rewritten

=j ^{* 1}. J_f nm -j r^Ted . J •_f n nm red ( 4 ) where f_{nm red} e M^6_LG"'™' is a vector that contains all non—zero elements of f_nm ( N_meas being the number of measured wrench components) and J_r ^T _ei is a reduced version of the Jacobian transpose in which all col umns corresponding to the measured components of wrench have been removed. Note that with N_DoF being the number of manipulator degrees of freedom (DoF) , Hence, J_r ^T _ed has more rows than col umns. This redundancy allows to improve the quality of F/T estimation for the remaining (non-measured) components of wrench. To this end, we assume that joint load estimates £_ext are available. They can e.g. be obtained from

where r_mot are motor torques, G{q) are gravity- induced torques, r_Jfiv represents dynamic feed forward and i_)Hc are friction torques obtained from a friction model. Furthermore, we assume

i.e. the error in joint load torque estimates is normally distributed with zero mean. Assuming that motor torques and gravity compensation are known very accurately, the covariance matrix å can be obtained by determining the standard deviation in the friction model error for each joint (e.g. by gathering joint load torque estimates during a val idation motion with no external load and a defined tool) . Considering (4) with the joint level uncertainty and an additional uncertainty in the low-dimensional F/T measurements from built-in sensors such as 10, we obtain

With this prior information in joint space, the re maining components of wrench can be estimated by maximum likelihood estimation as

This expression can be simplified under certain conditions, e.g. if the uncertainty of the measured components is neglected, re duces

If no data on the covariance matrix å. are availa ble, it can be necessary to replace it by an iden tity matrix I_N , implicitly assuming that the quality of the friction model is the same for all joints. Equation (9) then boils down to

which corresponds to the standard pseudo- inverse of the Jacobian transpose .

Alternatively, qualitative information with respect to the quality of the friction model can be used. To do so, the diagonal elements corresponding to main joints can be set to larger values than the elements corresponding to wrist joints (only the ratio of the elements matters for estimation) .

According to a second approach for combining meas ured and calculated wrench component, a first esti mate of wrench is calculated without regard to measurements, using the expression

In a next step, a second estimate of wrench is cal culated. In this step, all forces and torques that can directly be measured are replaced by the corre sponding measurements. For non—measured directions, the original estimates are kept. This is formalized as

if component i is measured

(12) if component i is not measured

A covariance matrix in Cartesian space is con- structed as its diagonal elements being defined as if component i is measured

(13) component i is not measured

wherein &_s ² _ensi is the variance of the sensor 10 and /_max; ^t^^ie maximum expected magnitude of the force or torque in direction i.

A refined estimate of the wrench is then obtained based on the first estimate of eq. (11) by a maxi mum a-posteriori estimation:

According to a third approach, joint level load torque information r_ext and the measurements gath ered from a low-dimensional F/T sensor such as sen sor 10 are combined into an augmented measurement vector y . This vector y has N_DoF ⁺N_meas components, N_DoF being the number of degrees of freedom of the robot, and N_meas being the number of measured compo nents of the wrench. Movement of the robot is mod elled

where p = Mq is the generalized momentum and

by

where is a vector specifying which components of wrench can directly be measured. For example, if force in z -direction can be measured, the vector is A Kalman filter is implemented that has as

its state vector. As usual in the art, the Kalman filter predicts a future state vector L*⁺¹ based on the current one x^k using eq. 15. The prediction yields changes of both generalized momenta q and of wrench / . A discrepancies are calculated be tween the predicted and the measured values of the generalized momenta and of the at least one meas- ured component f_mi of the wrench. These discrepan cies are used for updating the status vector, as is common in the art, but as the amount of data is higher than in case of conventional prediction of forces and torques based on a dynamic model of the robot alone, without having recourse to force or torque measurements, precision is improved.

According to a fourth approach, in analogy to x_ex - J^Tf+e_j, , we define an augmented Jaco- bian so that

where e_s is the sensor measurement noise with co- variance matrix å_s , and the matrix C_sens describes the Cartesian directions (or linear combinations thereof) that are directly measured by a sensor such as 10. As in case of the first approach, a so lution for eq. 17 is obtained by a maximum likeli hood estimation, yielding Eq. 18 provides estimates for all components of the wrench f , including those that are directly- measured using sensor 10 or the like, so that by comparing the estimated values to the measured ones, reliability of the underlying model can be j udged .

Reference numerals

1 robot arm

2 controller

3 base

4 end effector

5 link

6 joint

7 axis

8 drilling head

9 socket

10 sensor

11 TCP

Claims

1. A method for estimating a wrench acting on a reference point of a robot, comprising the steps of

a) measuring at least one, but not all com- ponents of the wrench, and

b) estimating non-measured components of the wrench based on a dynamical model of the robot while taking the measured components into ac count .

2. The method of claim 1, wherein step b) com prises a maximum- likelihood estimation of the non-measured components .

3. The method of claim 1, wherein step b) com prises calculating a first estimate of the wrench based on the dynamical model alone, and refining the first estimate using a maximum-a- posteriori estimation.

4 . The method of claim 1, wherein the wrench is predicted by a Kalman filter and the at least one measured component is input as a state measurement into said Kalman filter.

5. The method of one of the preceding claims, wherein among the measured components of the wrench there is at least one force component and/or among the non-measured components there is at least one torque component.

6. The method of one of the preceding claims in which the number of measured components is 1.

7. The method of one of the preceding claims wherein the measured component is parallel to a surface normal of a surface of the robot which extends through the reference point or to a direction in which the reference point advances when processing a workpiece.